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Old 04-01-2013
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Re: The physics of a mooring ball...

Not exactly your question, but possibly of interest?
Cruising off the grid (uncharted atoll interiors) we found we could not use traditional anchoring techniques when anchored in sand with large coral heads rising to near the surface (10 feet down in 30 to 50 feet of water) around the sandy spot. As the tide changed we would wrap the chain around one or more heads in a day and end up with zero scope.
I switched to a short chain of 30 feet and line from there. After setting the anchor I would use a large fender to float the chain as high as possible and place smaller floats on the line at intervals of about 10 feet.
It worked like a charm, never dragging and no more wrapping around the coral heads.
One likes this.
"Any idiot can make a boat go; it takes a sailor to stop one." Spike Africa aboard the schooner Wanderer in Sausalito, Ca. 1964.
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Old 04-01-2013
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Re: The physics of a mooring ball...

A 2' diameter buoy could if submerged displace 200 lb of water roughly.
The simple way of thinking of it so far as I see it is that in strong winds with lengthy scope of say 10;1 for simplicity the wind force is predominant and is trying to make the warp a horizontal line. It can't in effect because the buoyancy holds one end up.
Simplifying it with a long warp and say depth of 20' approximately 10% of the force is downward.
With a wind force of say 2000 lb that is the equivalent of 200 lb plus the weight of the chain say another 200 lb which is fair force downwards. Without the buoy you would get greater plunging down more or less equivalent to someone standing on the bow. But equally the bow would rise less so it would be wetter.
I don't think it would make much difference to the caternary as one end of the chain is supported by either the buoy or the bow and the weight of the chain remains the same.
When the wind is strong enough the chain is taut i.e at a fixed angle.
As it lessens in lulls with any stretch from the warp but not chain would relax giving some forward motion due entirely to the horizontal component. This would not be influenced by the buoy.
So on this sleepless night I don't see much change in the to and fro but in the bow being less inclined to dig in but more inclined to lift ie less wet. Of course if the waves are of reasonable size compared to the depth the rise means the boat moves forward and back with the fall so that motion would be slightly more but not that much if the waves are much less than the depth.
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